Related papers: Small Majorana Fermion Codes
Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize…
We present a bosonization procedure which replaces fermions with generalized spin variables subject to local constraints. It requires that the number of Majorana modes per lattice site matches the coordination number modulo two. If this…
Recently, Majorana Fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation (TQC). They are proposed to exist in various two-dimensional (2D) topological…
In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes…
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem…
It has been shown previously that a finite-length topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, realizes a one-dimensional topological…
We study the Majorana bound states arising in quasi-one-dimensional systems with Rashba spin-orbit coupling in the presence of an in-plane Zeeman magnetic field. Using two different methods, first, the numerical diagonalization of the…
Stabiliser codes with large weight measurements can be challenging to implement fault-tolerantly. To overcome this, we propose a Floquetification procedure which, given a stabiliser code, synthesises a novel Floquet code that only uses…
Detection and manipulation of excitations with non-Abelian statistics, such as Majorana fermions, are essential for creating topological quantum computers. To this end, we show the connection between the existence of such localized…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…
We evaluate theoretically the possibility to realize Majorana zero modes in hybrid devices made from topological-insulator (TI) nanowires proximity-coupled to a superconductor. Such systems have been suggested as building blocks of future…
As the condensed matter analog of Majorana fermion, the Majorana zero-mode is well known as a building block of fault-tolerant topological quantum computing. This review focuses on the recent progress of Majorana experiments, especially…
In this paper, we study some codes of algebraic geometry related to certain maximal curves. Quantum stabilizer codes obtained through the self orthogonality of Hermitian codes of this error correcting do not always have good parameters.…
We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor and calculate the topological phase diagram as a function of the chemical potential and magnetic field. The non-trivial topological state…
Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle-hole symmetric, and spatially-separated end modes which are…
A critical overview is given, aimed at non-specialist audience, of the recent efforts to detect and manipulate Majorana fermions in solid state devices. It is argued that the experiments on semiconductor quantum wires proximity coupled to…
We construct fermionic conformal field theories (CFTs) whose spectra are characterized by quantum stabilizer codes. We exploit our construction to search for fermionic CFTs with supersymmetry by focusing on quantum stabilizer codes of the…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
Quantum error correction protects quantum information against decoherence provided the noise strength remains below a critical threshold. This threshold marks the critical point for the decoding phase transition. Here we connect this…